Several reports on Friday claimed Nasri is set to undergo a medical at Eastlands, ahead of signing a five-year deal.
No official word had been given on the potential transfer, but Mancini addressed the press ahead of City's game against Bolton this weekend.
"I hope that we can close very quickly now," Mancini said when asked about the Nasri situation during Friday's press conference. "I don't know the latest because my concentration is on the game."
Mancini expressed his frustration last week that the deal had not yet been completed and, asked if there has been progress since, Mancini said: "I hope. I hope we can complete our target. The season is long, it's hard, and we need [to do this]."
"The market is finished in ten days," he said. "We have a problem because we haven't sold other players, but we need players to complete the squad. Until we sell the players that are here, it's a problem."
Tottenham boss Harry Redknapp has indicated that he expects Adebayor to join on loan, but Mancini was coy when asked whether he thought that deal would go through. "I don't know," he said. "It's possible."
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